Mirzazadeh Ramin, Eftekhar Azam Saeed, Mariani Stefano
Department of Civil and Environmental Engineering, Politecnico di Milano, Piazza L. da Vinci 32, 20133 Milano, Italy.
Department of Civil Engineering, University of Nebraska-Lincoln, 2200 Vine St, Lincoln, NE 68503, USA.
Sensors (Basel). 2018 Apr 17;18(4):1243. doi: 10.3390/s18041243.
Microscale uncertainties related to the geometry and morphology of polycrystalline silicon films, constituting the movable structures of micro electro-mechanical systems (MEMS), were investigated through a joint numerical/experimental approach. An on-chip testing device was designed and fabricated to deform a compliant polysilicon beam. In previous studies, we showed that the scattering in the input–output characteristics of the device can be properly described only if statistical features related to the morphology of the columnar polysilicon film and to the etching process adopted to release the movable structure are taken into account. In this work, a high fidelity finite element model of the device was used to feed a transitional Markov chain Monte Carlo (TMCMC) algorithm for the estimation of the unknown parameters governing the aforementioned statistical features. To reduce the computational cost of the stochastic analysis, a synergy of proper orthogonal decomposition (POD) and kriging interpolation was adopted. Results are reported for a batch of nominally identical tested devices, in terms of measurement error-affected probability distributions of the overall Young’s modulus of the polysilicon film and of the overetch depth.
通过数值与实验相结合的方法，研究了构成微机电系统（MEMS）可移动结构的多晶硅薄膜几何形状和形态相关的微观尺度不确定性。设计并制造了一种片上测试装置，用于使柔性多晶硅梁发生变形。在先前的研究中，我们表明，只有考虑到与柱状多晶硅薄膜形态以及用于释放可移动结构的蚀刻工艺相关的统计特征，才能恰当地描述该装置输入输出特性中的散射现象。在这项工作中，使用该装置的高保真有限元模型为过渡马尔可夫链蒙特卡罗（TMCMC）算法提供数据，以估计控制上述统计特征的未知参数。为降低随机分析的计算成本，采用了适当正交分解（POD）和克里金插值的协同方法。针对一批名义上相同的测试装置，报告了多晶硅薄膜整体杨氏模量和过蚀刻深度受测量误差影响的概率分布结果。
